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- W2887950653 abstract "We present a self-contained proof of a strong version of van der Waerden’s Theorem. By using translation invariant filters that are maximal with respect to inclusion, a simple inductive argument shows the existence of “piecewise syndetically”-many monochromatic arithmetic progressions of any length k in every finite coloring of the natural numbers. All the presented constructions are constructive in nature, in the sense that the involved maximal filters are defined by recurrence on suitable countable algebras of sets. No use of the axiom of choice or of Zorn’s Lemma is needed." @default.
- W2887950653 created "2018-08-22" @default.
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- W2887950653 date "2019-12-11" @default.
- W2887950653 modified "2023-09-24" @default.
- W2887950653 title "Translation Invariant Filters and van der Waerden’s Theorem" @default.
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- W2887950653 doi "https://doi.org/10.1007/978-3-030-31106-3_6" @default.
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